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The connection between mathematics and
art goes back thousands of years. Mathematics has been
used in the design of Gothic cathedrals, Rose windows,
oriental rugs, mosaics and tilings. Geometric forms were
fundamental to the cubists and many abstract expressionists,
and award-winning sculptors have used topology as the
basis for their pieces. Dutch artist M.C. Escher represented
infinity, Möbius bands, tessellations, deformations,
reflections, Platonic solids, spirals, symmetry, and
the hyperbolic plane in his works.

Mathematicians and artists continue to
create stunning works in all media and to explore the
visualization of mathematics--origami, computer-generated
landscapes, tesselations, fractals, anamorphic art, and
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Simon Beck's Snow and Sand Patterns

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"3D Koch at Arc2000," by Simon BeckPattern made in snow with snowshoes.

This is from my Facebook album titled Reinterpretations. This means the photos have been modified using the well-known program by Adobe. In general I shrink the horizontal dimension, darken the highlights a little, increase the contrast, shift the blue/red balance towards the blue, and increase the colour saturation. The grid of hexagons was surveyed working outwards from the centre, then the fractal exterior was added. --- Simon Beck (http://www.facebook.com/snowart8848)

"Circles 16 at Arc2000 Lakes 2012," by Simon BeckPattern made in snow with snowshoes.

This was done using the faintly visible ghost of an earlier design on the same site. Enough was visible despite recent snow fall for me to be able to find the corners of the roughly triangular figures without having to do any surveying. One person likened this image to a crocheted doily, another to a crop circle. This was done in 2012 at ARC 2000 is a ski area in France. --- Simon Beck (http://www.facebook.com/snowart8848)

"Sierpinski Triangle," by Simon BeckPattern made in snow with snowshoes.

This work is a variation on a Sierpinski Triangle. The S Triangle is a simple iterative process. Start with the largest triangle, find the midpoints of each edge, draw another triangle linking the midpoints, resulting in 4 triangles, then leave the middle triangle alone and repeat the process on the 3 other triangles. --- Simon Beck (http://www.facebook.com/snowart8848)

"Snow Pattern #5 at ARC 2000," by Simon BeckPattern made in snow with snowshoes.

The attempt at the 3D effect has been reasonably successful except where I ran out of reasonably flat snow! These bluish pictures have been processed in Photoshop and distorted to improve the proportions. This was done with Roberto Lebel at ARC 2000, a ski area in France. --- Simon Beck (http://www.facebook.com/snowart8848)

"Tsunami Memorial," by Simon BeckPattern made in snow with snowshoes.

The design(s) are a 5 pointed version of the 'snowflake curve' named by the German mathematician Von Koch. A lot of the inspiration for the snow art comes from the gardens in the temples in Kyoto, where sand is raked in patterns that are the closest thing I have seen elsewhere to the effect I achieve with snow. This work, created on the reservoir at Arc2000, took somewhere between 10 and 15 hours, and was completed in March 2012. On my Facebook there is an incomplete version of this photo that shows the skeleton of the smaller 5-pointed figures, that shows how this has been done. --- Simon Beck (http://www.facebook.com/snowart8848

"Mandelbrot set in the sand," by Simon Beck (https://www.facebook.com/snowart8848/) Pattern made of footprints in the sand at Brean Down in the U.K. Find a time lapse video of the creation at http://youtu.be/MVzGyAAtHiU --- Simon Beck (https://www.facebook.com/snowart8848/)

"Mandelbrot set in the sand, view two" by Simon Beck (https://www.facebook.com/snowart8848/) Pattern made of footprints in the sand at Brean Down in the U.K. Find a time lapse video of the creation at http://youtu.be/MVzGyAAtHiU --- Simon Beck (https://www.facebook.com/snowart8848/)

"Serpinski Triangle at Peisey-Vallandry," by Simon Beck (https://www.facebook.com/snowart8848/)Pattern made in snow with snowshoes at Peisey-Vallandry. --- --- Simon Beck (https://www.facebook.com/snowart8848/)